Modal control of unstable boiling states in three-dimensional nonlinear pool-boiling

Abstract

Topic is feedback stabilisation of a nonlinear pool-boiling system in three spatial dimensions (3D). Regulation of its unstable (non-uniform) equilibria has great potential for application in micro-electronics cooling and thermal-management systems. Here, as a first step, stabilisation of such 3D equilibria is considered. A control law is designed that regulates the heat supply to the heater as a function of the Fourier-Chebyshev modes of its internal temperature distribution. This admits a controller that is tailored to the system dynamics, as these modes intimately relate to the physical eigenmodes. The internal temperature distribution is, similar to practical situations, estimated from a finite number of measurement positions on the heater surface by an observer. Performance of this output-based modal controller is demonstrated and analysed by simulations of the nonlinear closed-loop system. This provides first proof of principle of the proposed control strategy for the regulation of 3D boiling states.